Acylindrical beam of particles each with charge q and mass m has a uniform initial (charge) density p and radius r. each particle in the beam is initially traveling with velocity v parallel to the beam's axis. consider the stability of this beam by examining the forces on a particle traveling in the beam at a distance r < r from the axis (the center of the cylinder). find the approximate force on a particle at radius r caused by the other particles in the beam. you will need to use gauss's law to calculate the electric field at radius r. describe your work, and do not skip steps; show that you understand gauss's law.

Stars x and y are both bluish main sequence stars. star x has a higher absolute brightness than star y. how do the two stars compare? explain

The pressure, volume, and temperature of a mole of an ideal gas are related by the equation pv = 8.31t, where p is measured in kilopascals, v in liters, and t in kelvins. use differentials to find the approximate change in the pressure if the volume increases from 14 l to 14.6 l and the temperature decreases from 375 k to 370 k. (round the answer to two decimal places.)

Glass is transparent to visibile light under normal conditions; however, at extremely high intensities, glass will absorb most of the light incident upon it. this works through a process known as multiphoton absorption. in this process, several photons are absorbed at the same time. if very intense light whose photons carry 2ev of energy is shined onto a material with a band gap of 4ev, that light can be absorbed through two-photon absorption, because two photons have the right amount of energy to bridge the band gap. what is the minimum number of photons of 800-nm light that are needed to equal or exceed the band gap of fused silica glass